Dynamics of meromorphic functions with direct or logarithmic singularities
Dynamics of meromorphic functions with direct or logarithmic singularities
Let f be a transcendental meromorphic function and denote by J(f) the Julia set and by I(f) the escaping set. We show that if f has a direct singularity over infinity, then I(f) has an unbounded component and I(f)∩J(f) contains continua. Moreover, under this hypothesis I(f)∩J(f) has an unbounded component …